Discrépance de la suite ({nα}),α=(1+5)/2
Annales de l'Institut Fourier, Tome 29 (1979) no. 1, pp. 81-106.

Soit D*(N) la discrépance “à l’origine” de la suite n1+52. Nous montrons que lim supD*(N)LogN=320Log1+52-1=0.31⋯, quantité inférieure à celle correspondant à la suite de van der Corput. Les techniques utilisées sont celles liées au développement en fraction continue.

Let D*(N) be the star-discrepancy of the sequence n1+52. We show that lim supD*(N)LogN=320Log1+52-1=0.31⋯, which illustrates the fact that our sequence has smaller star-discrepancy than that of van der Corput’s sequence. Our proofs involve continued fraction theory.

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Dupain, Yves. Discrépance de la suite $(\lbrace n\alpha \rbrace ),\alpha =(1+\sqrt{5})/2$. Annales de l'Institut Fourier, Tome 29 (1979) no. 1, pp. 81-106. doi : 10.5802/aif.728. https://numdam.org/articles/10.5802/aif.728/

[1] R. Bejian et H. Faure, Discrépance de la suite de van der Corput, C.R. Acad. Sc., Paris, 285 (1977), 313-316. | MR | Zbl

[2] Y. Dupain, Intervalles à restes majorés pour la suite {nα}, Acta. Math. Acad. Scient. Hung., t. 29 (3,4) (1977), 289-303. | MR | Zbl

[3] L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Wiley Interscience, New York, (1974), 88-132. | MR | Zbl

[4] J. Lesca, Sur la répartition modulo 1 des suites {nα}, Acta Arith., 20 (1972), 345-352. | MR | Zbl

[5] J. Lesca, Sur la répartition modulo 1 des suites {nα}, Séminaire Delange-Pisot-Poitou, (1966-1967), fascicule 1, exposé n° 2. | Numdam | Zbl

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